Yes, you need to obtain confirmation of results from WAEC in addition to what you already have:
You are strongly encouraged to verify these documents at source, through the West African Examinations Council’s online system at
www.ghana.waecdirect.org. The student provides you with a PIN number that they purchase for the equivalent of $3 (available at post offices or WAEC regional offices), that is used to retrieve a printable copy of their WAEC results. This is the fastest and most reliable way of verifying a student’s results from Ghana. All results from all WAEC exams dating back to 1993 can be verified through WAECDirect.
https://gh.usembassy.gov/education-culture/educationusa-center/educational-system-ghana/
As an aside, I find it strange your wife is unable to obtain her college certificate 13 years after graduation due to administrative errors on the school’s side.